Question

a function $h(x)$ is described in the table below. fill in the table for $h^{-1}(x)$.

$x$ (input)	$y$ (output)
$7$	$-9$
$-5$	$5$
$-8$	$1$
$-3$	$7$
$-6$	$6$

Explanation:

Step1: Recall inverse function table rule

For a function \( h(x) \) with input \( x \) and output \( y \), the inverse function \( h^{-1}(x) \) will have input \( y \) and output \( x \). So we swap the \( x \) (input) and \( y \) (output) columns of the original table.

Step2: Process each row

• Original row 1: \( x = -4 \), \( y = -4 \). For \( h^{-1}(x) \), input \( y = -4 \), output \( x = -4 \).
• Original row 2: \( x = 7 \), \( y = -9 \). For \( h^{-1}(x) \), input \( y = -9 \), output \( x = 7 \).
• Original row 3: \( x = -5 \), \( y = 5 \). For \( h^{-1}(x) \), input \( y = 5 \), output \( x = -5 \).
• Original row 4: \( x = -8 \), \( y = 1 \). For \( h^{-1}(x) \), input \( y = 1 \), output \( x = -8 \).
• Original row 5: \( x = -3 \), \( y = 7 \). For \( h^{-1}(x) \), input \( y = 7 \), output \( x = -3 \).
• Original row 6: \( x = -6 \), \( y = 6 \). For \( h^{-1}(x) \), input \( y = 6 \), output \( x = -6 \).

Step3: Construct the inverse function table

The table for \( h^{-1}(x) \) will be:

\( x \) (Input for \( h^{-1} \))	\( y \) (Output for \( h^{-1} \))
-9	7
5	-5
1	-8
7	-3
6	-6

Answer:

The table for \( h^{-1}(x) \) is as constructed above (with input -4, -9, 5, 1, 7, 6 and output -4, 7, -5, -8, -3, -6 respectively).